A fast symmetric SVD algorithm for square Hankel matrices

This paper presents an O(n2logn) algorithm for computing the symmetric singular value decomposition of square Hankel matrices of order n, in contrast with existing O(n3) SVD algorithms. The algorithm consists of two stages: first, a complex square Hankel matrix is reduced to a complex symmetric tridiagonal matrix using the block Lanczos method in O(n2logn) flops; Second, the singular values and singular vectors of the symmetric tridiagonal matrix resulted from the first stage are computed in O(n2) flops. The singular vector matrix is given in the form of a product of three or two unitary matrices. The performance of our algorithm is demonstrated by comparing it with the SVD subroutines in Matlab and LAPACK.